Why were the drawings of Colossus burnt after WW2 and why was its very existence "of course" kept secret?

Just to give a concise, general answer: the destruction of the documents was obvious (“of course”) to your author because the end of a single war does not mean the end of all wars. The British government had to be alert to the possibility of another war, perhaps quite soon (a possibility that was not unthinkable). To maintain their advantage, no matter what might happen, they kept everything as secret as possible.

With the passage of time these restrictions seem quaint, especially given how open cryptographic technology has become, but from their perspective at the time, it makes perfect sense.

Question:
Why were the drawings of Colossus burnt after WW2 and why was its very existence “of course” kept secret?

There are a number of reasons often cited to explain why the breaking of Ultra was kept secret until the 1970's. These reasons cover why all avenues of Bletchley Park's efforts were kept secret, including Colossus. Colossus an early computer partially designed by Alan Turing widely considered to be the father of theoretical computer science and artificial intelligence. Colossus was built to optimize reading ultra communications, which were first cracked by the British in May of 1940 by use of the electro-mechanical device called the "bombe". Colossus was made to speed the reading of Ultra communications later in the war( mk1- Dec 1943, mk2 June of 1944 ). Colossus's existence was deemed a threat to expose the vulnerability of Ultra.

Reasons:

1. Because the ability to read Ultra, or more generally, Rotor encryption devices remained useful to the British for decades after VE Day. Rotor encryption devices remained widely in use up into the 1970s as few knew they were not secure. The British themselves were involved in selling surplus devices or permitted Germany to do so after WWII, encouraging their use. The United States NSA used such devices:

   • SigABA retired in the 1950s
   • KL-7). retired in the 1980s; The last Canadian message encrypted with a KL-7 was sent on June 30, 1983.

   The Swiss had their own version of the enigma rotor encryption device, the NEMA, declassified in 1992. Japan used Purple rotor encoding machine. In the 1970s, computer technology became more prevalent, and Rotor encryption devices quickly became obsolete, making the secret less valuable.

   Ultra
   David Kahn pointed out in his 1974 New York Times review of Winterbotham's The Ultra Secret, after the war, surplus Enigmas and Enigma-like machines were sold to Third World countries, which remained convinced of the security of the remarkable cipher machines. Their traffic was not as secure as they believed, however, which is one reason the British made the machines available

   A software implementation of a rotor machine was bundled with Unix. It was used in the crypt command that was part of early UNIX operating systems. It was among the first software programs to run afoul of U.S. export regulations which classified cryptographic implementations as munitions.

2. Just after WWII there was some trepidation that Axis countries would use the breaking of Ultra as an excuse for their defeat.

   From Ultra by Winterbotham in "The Ultra Secret (1974)", recounts that two weeks after V-E Day, on 25 May 1945, Churchill requested former recipients of Ultra intelligence not to divulge the source or the information that they had received from it, in order that there be neither damage to the future operations of the Secret Service nor any cause for the Axis to blame Ultra for their defeat. Winterbotham, F. W. (1974), , New York: Harper & Row, ISBN 0-06-014678-8

3. Fear on the part of the British that the United States and Soviet Union would be offended they weren't officially made part of the secret.
   The Historical Impact of Revealing the Ultra Secret pg 27 second column

4. In the 1920s, Churchill was involved in an event which used information obtained from a broken Soviet code to expel a Soviet trade delegation. While participating in trade discussions, the Soviets were collecting intelligence, spying in London. Specifically they had obtained a British Code book. The British thanks to signals intelligence, discovered this breach, and ultimately expelled of Soviet diplomatic delegation. The Soviets realizing their code had been broken set about changing and strengthening their codes. This in turn led to an intelligence blackout for the British for a decade. This event, in which Winston Churchill was a central character, continued to make the British government vigilant about all potential disclosures of code breaking, as they could lead to serious impacts to it's capabilities, as had occurred in the 1920s; in what ultimately was deemed a trivial breach of etiquette.

   How 1920s British spy agency files reveal a proto-Cold War rife with intrigue
   It was counter-productive on the most basic level: to bring the case to expel the Russians—which, ironically, had as its excuse the theft of a very basic British army signals manual—the British government revealed to the Russians that they could decode their telegrams. Of course the Soviets immediately changed their codes and we could no longer decrypt them for over a decade.

Epologue

Not really part of the answer but I think a real tragedies occurred tangentially to this question. I mentioned Alan Turing who is widely considered the father of the modern computer science and Artificial Intelligence. Turing designed and constructed a electro mechanical device he called "the bombe", to defeat enigma in May of 1940 and contributed to the design of Enigma which optimized reading enigma messages later in the war. Many people believe that Bletchley Park shortened by more than a year and millions of lives were saved. The tragedy was that after WWII Turing was charged with being a h*m*sexual (1952) and at his trial the prosecution played up that Turing had not served in the war effort, had not done service to his country in time of war in condemning him. The court found him guilty and ordered him to take medication. Both of which it is believed contributed to his suicide in 1954. Because Ultra and Bletchley park were so secret, no one spoke up for Turing in his criminal case after the war and Turing could not speak up for himself, bound by secrecy acts.

• Prime Minister, Gordon Brown, apologized on behalf of the British government for the treatment of Turing September 10, 2009.
• In Dec 2013 The Queen granted Turing a Royal Pardon.

In September 2016, the government announced its intention to expand this retroactive exoneration to other men convicted of similar historical indecency offences, in what was described as an "Alan Turing law".[181][182] The Alan Turing law is now an informal term for the law in the United Kingdom, contained in the Policing and Crime Act 2017, which serves as an amnesty law to retroactively pardon men who were cautioned or convicted under historical legislation that outlawed h*m*sexual acts.

To understand why the Ultra secret had to be kept secret, one has to look at the encryption technology that was in use during the post war period, and in many cases is still in use today. Although we may consider the German Enigma machines just technology from the second world war, most people never imagined that that technology continued to be in use for much Government and military message traffic.

As evidence I cite the British Typex machines which were in use to the mid 1950's. The American KL-7 which was in use by NATO until 1983, the Russian Fialka which was kept secret until 2005, and the Swiss NEMA which was declassified in 1992. All these machines use rotor wheel technology just as the Enigma did. The methods of attacking the different varieties of Enigma performed at Bletchley Park would still have value in leveraging other forms of rotor machines in use.

Quite clearly, if Britain and their Allies were using similar encryption systems that they knew could be vulnerable they would not want others to acquire that technology. If, during the Cold War, the eastern block was using similar technology it was in GCHQ's interest that they did not develop a need to develop new encryption technology. If other states were purchasing and using Swiss machines, no one would want that equipment to fall out of favour for some other method that was more resistant to the forms of attack developed as part of the Ultra Secret.

The secret was kept well because many understood why it had to remain a secret. As the rumours started to leak out in various books and publications, the details became more and more explicit. Some critical details, however, remained secret and it was enough to protect secret of the vulnerabilities of rotor based mechanisms for now. Eventually when so much time had passed it was believed that everything could be spoken about, as there was nothing left to hide. One publication^* is believed to have lifted that last veil from which cascaded the obsolescence of rotor based machines in the 1980s. Much to the chagrin of GCHQ and NSA the genie was out of the bottle.

That is why the machines had to be destroyed and the Ultra Secret kept^#.

Epilogue

This issue is still extant today. One only has to consider the latest news regarding the CIA and Cryto AG. Their machines are all rotor based also. I think the media fails to understand the nature of the compromise of the Hagelin based machines. That weakness is Tunny and it is not in the machines but in the method of attack. But perhaps I digress...

^* The Hut Six Story by Gordon Welchman in 1982, which caused him to lose his security clearance and his job. He never really understood why, because those on the inside of the security system couldn't tell him. They will never confirm or deny.

^#My opinion, based on long years of cordial conversations with my good friend the late Dr. Hale (late of Hut 6) and others.

To answer why they denied its existence, because the value of British code breaking relied on keeping their ability to break codes secret. (Sorry this is without sources, I'm on a phone on a train.)

Part of the wild success of British code breaking during the war was due to the Germans never realizing their communications were compromised. The Germans continued to send vital information using encryption that the British could read and use rapidly.

While the Germans often suspected their codes were broken, and made some improvements, they considered the issue from their own relatively unsophisticated code breaking ability. Had they realized the extent of British capabilities, they likely would have beefed up their encryption and transmitted less.

GCHQ's leap forward in code breaking ability cannot be overstated. Before WW2, code breaking was considered like solving a crossword puzzle. You got a bunch of very clever people together and they figured it out. GCHQ made breaking codes about mathematics and statistics. They turned it into a massive organization able to quickly and systematically process high volumes of traffic and have it disseminated that same day.

Just as great a leap was their use of mechanisation. They built analog and digital computers like the bombes and Colossus of speeds and sizes and quantities unheard of. If the world knew about machines like Colossus they would have beefed up their security. Though burning the plans was probably a bit much.

Keeping these capabilities secret would continue to help Britain after the war, snooping on other countries' domestic and military traffic. Secrecy was so ingrained into British code breakers that when the first popular (and extremely flawed) book was published about it, The Ultra Secret in 1974, it was considered a betrayal by some veterans of GCHQ despite the world now being well into the computer age.